Simplifying — substitution and multiplication of expressions

We need to evaluate $5x-3$ when $x=4$. This means we replace the variable $x$ with the number $4$.

Replace $x$ with $(4)$: $5(4)-3$

Following order of operations, multiply before subtracting: $5\times 4=20$, so we get $20-3$.

$20-3=17$. The correct answer is 17.

We need to substitute $x=4$ into $5x-3$ and compute the numerical result.

20 would result from computing $5\times 4=20$ and forgetting to subtract 3. This is an incomplete calculation.

23 would result from adding 3 instead of subtracting: $20+3=23$. This misreads the minus sign as a plus.

12 might come from incorrectly computing $(5-3)\times 4=8$ or another order-of-operations error. It does not match the correct calculation.

$5(4)-3=20-3=17$. The correct answer is 17.

We need to evaluate $a^2+3a$ when $a=-3$. Using brackets around the substituted value is important when dealing with negatives.

Replace $a$ with $(-3)$: $(-3{)}^2+3(-3)$

$(-3{)}^2=(-3)\times (-3)=9$. A negative times a negative gives a positive result.

$9+3(-3)=9+(-9)=9-9=0$.

The expression equals 0 when $a=-3$.

We substitute $a=-3$ into $a^2+3a$ and must handle negative numbers and powers carefully.

18 could arise if someone computes $(-3{)}^2=9$ and then adds $3\times 3=9$ incorrectly (forgetting the negative on $a$), giving $9+9=18$. This ignores the negative value of $a$.

−18 could come from mistakenly computing $(-3{)}^2=-9$ (a common error), then $-9+(-9)=-18$. But $(-3{)}^2=+9$, not $-9$.

−9 might result from computing $9-18=-9$ after an arithmetic slip. The correct multiplication gives $3\times (-3)=-9$, and $9+(-9)=0$, not $-9$.

$(-3{)}^2+3(-3)=9+(-9)=0$.